The billionaire's lawyers deny any wrongdoing and have told the press that they are confident their client will not face charges, pointing out that police did not seize his passport.
JD.com's rules require Liu, who holds almost 80 per cent of the company's voting rights, to be present at board meetings for the board to make decisions, although it was not clear if he has to be physically present or could participate by teleconference.
It gave no further details, but Mr Elder said the alleged attack reportedly occurred at 1 am local time on Friday and that Mr Liu was taken into custody later that evening.
Zhang Shuhan, a JD.com official, said Monday by phone that "Liu Qiangdong has been released without charges and he is now back in China". Liu was released from police custody without bail or travel restrictions.
The reason for Mr Liu's arrest in the United States was initially disclosed as "criminal sexual conduct". It said the alleged offence was "criminal sexual contact - rape", and said domestic violence was not involved. "There's no credible complaint", defense attorney Joseph Friedberg said on Tuesday.
According to Minnesota law, the maximum penalty if found guilty of first degree sexual assault is 30 years and the minimum is 12 years.
Liu was released without being charged after his arrest on Friday and has returned to China.More news: ‘American Horror Story: Apocalypse’: The Anti-Christ Arrives in Full Trailer
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Shen Meng, director of boutique investment bank Chanson & Co, said as a US-listed company, the statement from JD is not professional and if the company is really involved in issuing materially misleading business information to the investing public, it might be punished severely or even be delisted from the USA bourses.
Liu was in Minneapolis because he is enrolled in a doctorate of business administration program at University of Minnesota's Carlson School of Management.
Three American law firms are organizing class action lawsuits on behalf of the shareholders of Chinese e-commerce giant JD.com after rape allegations against the company's chairman caused its share prices to tumble.
Liu, a married father-of-two, is said to be worth an estimated $7.9billion.
If the USA police accuse Liu, the company's share price would continue to fall, but it was predicted that there would not be a sharp crash due to an already sharp decline this year, Reuters quoted Danny Law, an analyst at brokerage Guotai Junan as saying.
In July, an Australian court lifted the suppression order that allowed Liu's name to be made public in connection a 2015 party at the billionaire's Sydney penthouse.